Evidence of Nonperturbative Continuum Correlations in Two-Dimensional Exciton Systems in Semiconductor Microcavities

Abstract

In nonlinear semiconductor optics, two-particle scattering is often being modeled successfully within the second Born approximation (2nd BA) of the Coulomb interaction. It is shown in this paper that, at low energies, such a perturbative treatment of Coulomb correlations applied to exciton-exciton scattering in two-dimensional systems fails even qualitatively (unless phenomenological or self-consistent dephasing processes are included in the theory). We show that the failure of the 2nd BA in two dimensions can be inferred from a comparison of our theoretical results with reported experiments of four-wave mixing signals from semiconductor microcavities.Linear excitonic absorption effects (see, e.g., [1]) and optical nonlinearities arising from exciton-exciton interactions in quasi-one-, two-, and three-dimensional semiconductors are well established (see, e.g., [2][3][4]). While the dimensionality dependence of linear excitonic effects is well understood (the simplest example being the increase of exciton binding energy with decreasing dimensionality), that of nonlinear excitonic effects is in general not clearly established. In this Letter, we discuss one aspect of this issue which concerns exciton-exciton scattering at low kinetic energies. Such scattering processes are commonly treated within the second Born approximation (2nd BA), because this approximation can already account, at least qualitatively, for all observable signatures of excitonexciton scattering in nonlinear optical experiments. Moreover, numerous experiment-theory comparisons (including cases involving exciton-free-carrier scatterings) seem to validate the 2nd BA. Examples include the line shape of optical gain spectra in semiconductor lasers [5], photoluminescence from semiconductor quantum wells [6], and optical Stark shifts in semiconductor quantum wells [7].While we do not dispute the validity of the model assumptions underlying those experiment-theory comparisons, we will show in the following that the 2nd BA in two dimensions should be used with caution. In fact, if the theoretical results are not smoothened by phenomenological or self-consistently calculated [6] dephasing rates, the 2nd BA T matrix (or scattering amplitude) governing low-energy exciton-exciton scattering would diverge in the limit of zero exciton center-of-mass-motion energies, while the exact scattering amplitude is known to vanish as 1͞ln͑energy͒ in the same limit [8]. These behaviors result from the dimensionality of the system and hold for any generic short-ranged potential independent of strength and other details. In analyzing semiconductor experiments, including the ones referenced above, dephasing introduced into the theory regularizes these nonanalytic behaviors, but their presence is still indicated by the large deviation of the 2nd BA T matrix from the exact one even for only moderately strong potentials (below, we will show this in more detail, cf. Fig. 2). Admittedly, since this deviation is quantitative instead of qualitative, its effects may not be ascertai...

Influence of exciton-exciton correlations on the polarization characteristics of polariton amplification in semiconductor microcavities

“…No additional assumptions for the effective polariton-polariton interaction are needed, which is directly included in our theory via the frequency dependent and complex exciton-exciton scattering matrices. 10 Our theoretical analysis incorporates: (i) the well-established microscopic many-particle theory for the optically-induced QW polarization dynamics based on the dynamics-controlled truncation (DCT) formalism 26,27 , and (ii) the self-consistent coupling of this dynamics to the dynamics of the optical fields in the cavity modes 10,28,29 including all vectorial polarization state channels. The theory consistently includes all coherent third order (χ (3) ) nonlinearities and the resulting equations of motion are solved in a self-consistent fashion in the optical fields which includes a certain class of higherorder nonlinearities.…”

“…1), we account for the dominant contributions to the QW response by evaluating the optically induced QW polarization in the 1s heavy-hole exciton basis. 29,31,32,34 We start from the coupled equations of motion for the field E k in the cavity modes with in-plane momentum k (treated in quasi-mode approximation 35 ) and the optically induced interband polarization amplitude p k in the embedded QW. We formulate our theory in the TE-TM basis for the optical fields in the cavity, Fig.…”

Coherent and incoherent aspects of polariton dynamics in semiconductor microcavities

“…This coherent term originates from the non-Markovian nature of the exciton-exciton interaction when going beyond the usual Hartree-Fock approximation and corresponds to four-particle correlations [22]. Lastly, several state of the art microscopic calculations show that the EID strength is highly energy dependent and becomes large when the energy of the two scattered polaritons exceeds twice the exciton energy [23][24][25][26][27]. This might also explain the onset of the lower polariton EID towards positive cavity detuning.…”

Coherence and correlation in semiconductor microcavities

“…Γ describes the dephasing of two pair coherences (in the following we will use Γ = 2πγ x ). We calculated F (τ ) for QW excitons following a recent microscopic approach [12,13] based on the T-matrix. By this approach the 4-particle states |E m are expanded in terms of exciton-pairs on the 1s parabola.…”